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Are there exactly solvable CFTs?

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I am wondering if there are CFTs such that n-point correlation functions in them of the fields (may be the primaries or of some notion of twist fields) is exactly known.

Are there such?
Aren't minimal models supposed to have this property?
Even if not exactly known, can the n-point functions (may be when written as a conformal block expansion) be written order-by-order as a power series in the central charge? (..I guess there is some theorem about the asymptotic exponential dependence of the conformal blocks on the central charge (reference help? ) and I want to know if 1/c corrections to that are known..)

This post imported from StackExchange MathOverflow at 2014-08-25 11:40 (UCT), posted by SE-user user6818

asked Oct 13, 2013 in Theoretical Physics by user6818 (960 points) [ no revision ]
retagged Nov 21, 2014 by dimension10

Are your $n$-point correlation functions in genus zero?

This post imported from StackExchange MathOverflow at 2014-08-25 11:40 (UCT), posted by SE-user S. Carnahan

commented Oct 13, 2013 by S. Carnahan (190 points) [ no revision ]

@S.Carnahan That would be the simplest scenario I would like to know of. (..if you can say something about higher genus then that is more exciting ;P..)

This post imported from StackExchange MathOverflow at 2014-08-25 11:40 (UCT), posted by SE-user user6818

commented Oct 13, 2013 by user6818 (960 points) [ no revision ]

Did you look at the work of Dotsenko and Fateev from mid 1980s. They computed correlation functions of a number of 2d conformal field theories.

This post imported from StackExchange MathOverflow at 2014-08-25 11:40 (UCT), posted by SE-user José Figueroa-O'Farrill

commented Oct 14, 2013 by José Figueroa-O'Farrill (2,315 points) [ no revision ]

@JoséFigueroa-O'Farrill Can you kindly refer to any paper that you have in mind? Is it known by some name that I can may be trace in the Francesco et. al's book?

This post imported from StackExchange MathOverflow at 2014-08-25 11:40 (UCT), posted by SE-user user6818

commented Oct 15, 2013 by user6818 (960 points) [ no revision ]

@user6818, I have lent my copy of the book by di Francesco et al., I'm afraid, but the papers I have in mind are the following: dx.doi.org/10.1016%2F0550-3213%2884%2990269-4 and dx.doi.org/10.1016%2FS0550-3213%2885%2980004-3 .

This post imported from StackExchange MathOverflow at 2014-08-25 11:40 (UCT), posted by SE-user José Figueroa-O'Farrill

commented Oct 15, 2013 by José Figueroa-O'Farrill (2,315 points) [ no revision ]

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